Journal article
Rigidity for critical points in the Lévy-Gromov inequality
- Abstract:
- The Lévy-Gromov inequality states that round spheres have the least isoperimetric profile (normalized by total volume) among Riemannian manifolds with a fixed positive lower bound on the Ricci tensor. In this note we study critical metrics corresponding to the Lévy-Gromov inequality and prove that, in two-dimensions, this criticality condition is quite rigid, as it characterizes round spheres and projective planes.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 373.4KB, Terms of use)
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- Publisher copy:
- 10.1007/s00209-017-1993-x
Authors
- Publisher:
- Springer
- Journal:
- Mathematische Zeitschrift More from this journal
- Volume:
- 289
- Issue:
- 3-4
- Pages:
- 1191-1197
- Publication date:
- 2017-12-07
- Acceptance date:
- 2017-10-14
- DOI:
- EISSN:
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1432-1823
- ISSN:
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0025-5874
- Language:
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English
- Keywords:
- Pubs id:
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pubs:1061588
- UUID:
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uuid:7762b322-c980-4dcb-9b26-53bb3fab8519
- Local pid:
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pubs:1061588
- Source identifiers:
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1061588
- Deposit date:
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2019-10-11
Terms of use
- Copyright holder:
- Cavalletti et al
- Copyright date:
- 2017
- Notes:
- © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- Licence:
- CC Attribution (CC BY)
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